Question

Please solve each of the inequalities and graph the solution on a number line. show work for number 4 and 5.
1. x – 3 > –9
2. –2x + 1 ≤ –11
3. 10 < –3x + 1
4. 2(x + 5) > 8x – 8
5. –2(x – 3) ≥ 5 – (x + 3)
Explain, in complete sentences, when you would use an open circle or a closed circle, and when you would shade to the right or left, to graph an inequality on the number line.

Answer 1

you use an open circle when the inequality doesnt have an "or equal to" part in it, like 4x>5 would be an open circle, but a closed circle is used when an inequality has an "or equal to" part to it, such as \[4x \ge5\]

Answer 2

you shade to the right or left by plugging in an arbitrary number that doesn't make the inequality equal on both sides. if that number satisfies the inequality, thats the way that you shade on the number line